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Solve Jar and Ball Puzzles

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Your question is Solve Jar and Ball Puzzles. Take a moment with it on the right.

Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).

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Problem

Solve these puzzles: (a) using 5-liter and 3-liter jars to measure 4 liters, and (b) with 50 white and 50 black balls across two bowls, maximize the probability of picking a white ball from both bowls.

Explain each step clearly, state any assumptions, and justify why the proposed ball distribution maximizes the probability. Be prepared to compare alternative approaches and communicate the result concisely.